Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
- URL: http://arxiv.org/abs/2311.00753v2
- Date: Wed, 17 Jan 2024 18:45:33 GMT
- Title: Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
- Authors: Budhaditya Bhattacharjee, Pratik Nandy, Tanay Pathak
- Abstract summary: We analytically establish the linear growth of two sets of coefficients for any generic jump operators.
We find that the Krylov complexity saturates inversely with the dissipation strength, while the dissipative timescale grows logarithmically.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We use Krylov complexity to study operator growth in the $q$-body dissipative
SYK model, where the dissipation is modeled by linear and random $p$-body
Lindblad operators. In the large $q$ limit, we analytically establish the
linear growth of two sets of coefficients for any generic jump operators. We
numerically verify this by implementing the bi-Lanczos algorithm, which
transforms the Lindbladian into a pure tridiagonal form. We find that the
Krylov complexity saturates inversely with the dissipation strength, while the
dissipative timescale grows logarithmically. This is akin to the behavior of
other $\mathfrak{q}$-complexity measures, namely out-of-time-order correlator
(OTOC) and operator size, which we also demonstrate. We connect these
observations to continuous quantum measurement processes. We further
investigate the pole structure of a generic auto-correlation and the
high-frequency behavior of the spectral function in the presence of
dissipation, thereby revealing a general principle for operator growth in
dissipative quantum chaotic systems.
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